Chapter 7, Problem 87PP

BIO Microraptor gui: The Biplane Dinosaur

The evolution of flight is a subject of intense interest in paleontology. Some subscribe to the “cursorial” (or ground-up) hypothesis, in which flight began with ground-dwelling animals running and jumping after prey Others favor the “arboreal” (or trees-down) hypothesis, in which tree-dwelling animals, like modern-day flying squirrels, developed flight as an extension of gliding from tree to tree.

A recently discovered fossil from the Cretaceous period in China supports the arboreal hypothesis and adds a new element—it suggests that feathers on both the wings and the lower legs and feet allowed this dinosaur, Microraptor gui, to glide much like a biplane, as shown in Figure 7-31 (a). Researchers have produced a detailed computer simulation of Microraptor, and with its help have obtained the power-versus-speed plot presented in Figure 7-31 (b). This curve shows how much power is required for flight at speeds between 0 and 30 m/s. Notice that the power increases at high speeds, as expected, but it is also high for low speeds, where the dinosaur is almost hovering. A minimum of 8.1 W is needed for flight at 10 m/s. The lower horizontal line shows the estimated 9.8-W power output of Microraptor, indicating the small range of speeds for which flight would be possible. The upper horizontal line shows the wider range of flight speeds that would be available if Microraptor were able to produce 20 W of power.

Also of interest are the two dashed, straight lines labeled 1 and 2. These lines represent constant ratios of power to speed—that is, a constant value for P/U Referring to Equation 7-13, we see that

P/v = Fv/v = F

, so lines 1 and 2 correspond to lines of constant force. Line 2 is interesting in that it has the smallest slope that still touches the power-versus-speed curve.

87. Estimate the minimum force that Microraptor must exert to fly

1. A.    A. 0.65 M
2. B.     B. 1.3 N
3. C.     C. 1.0 N
4. D.    D. 10 N